STATISTICAL ANALYSIS AND INFERENCE

As discussed in Section I, above, the distribution of regional cerebral blood flow (rCBF) is indexed by the accumulated counts over the scanning period. This reliably reflects flow in the physiological range (Fox and Mintun, 1989; Mazziotta et a l,

1985). SPMs are spatially extended statistical processes that are used to characterize regionally specific effects in imaging data. Statistical parametric mapping combines the general linear model (to create the statistical map, or SPM) and the theory of Gaussian fields to make statistical inferences about regional effects (Friston et a l,

1991; Friston et a l, 1994; Worsley et a l, 1992). The general linear model is:

“an equation that relates what one observes, to what one expected to see, by

expressing the observation (response variable) as a linear combination o f the

expected components (or explanatory variables) and some residual error ” (Friston, 1997).

The data were analyzed using a blocked one-way ANCOVA (Friston et a l, 1990). The design matrix included global activity as a subject specific confounding covariate. Subject and covariate effects were estimated according to the general linear model at each voxel (Friston et a l, 1995a). To test regionally specific condition effects, the estimates were compared using linear contrasts. The resulting set of voxel values for each contrast constituted a statistical parametric map of the t statistic SPM{t}. The search volume was from z = -48 mm to z = +60 mm (where - is inferior to the AC-PC line and + is superior to the AC-PC line). The general linear model generates a three dimensional statistical image comprising thousands of correlated t statistics. Therefore the probability for finding activations at any voxel needs to be corrected for multiple comparisons. SPMs are interpreted statistically with reference to the probabilistic behaviour of stationary (i.e. not a function of position) Gaussian

fields (Adler, 1981). Deviations of SPMs with reference to this field are interpreted as being regionally specific and associated with the independent variable manipulated experimentally.

Resulting foci are characterised in terms of “spatial extent” and “peak height”. This characterization is in terms of the probability that a region of the observed number of voxels or the peak height observed could have occurred by chance over the entire volume analysed (i.e. a corrected f-value).

Voxel locations are given in co-ordinates that correspond to the stereotactic atlas of Talairach and Toumoux (1988) and are reported in the order x (- is left, + is right), y (- is posterior to the anterior commissure line, + is anterior to the commissure line), z (- is inferior to the intercommissural line, + is superior to the AC-PC line). This order of co-ordinates is used for Tables displaying results in this thesis. Brain regions for these co-ordinates are always shown on the left column of the table, with corresponding Brodmann Areas (BA) where appropriate. Activation co-ordinates are shown on the right with Z-scores shown in bold type.

Where graphs of regional cerebral blood flow (rCBF) are shown in this thesis, rCBF responses are centred (origin = 0) on the mean global blood flow in the specified voxel. A unit of one is equivalent to a 2% blood flow increase and standard error bars are shown for each condition. Pictorial representations of activations are shown on 3D rendered brain images and axial brain slices (using the MNI standard brain or a mean image of the subjects’ MRI stmctural scans). These pictures are shown at varying thresholds, chosen to best illustrate the findings from the results.

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IV.a. Conjunction and Masking Procedures are Used throughout this Thesis

Conjunction analyses in SPM97 (Price and Friston, 1997) sum over the effects of each contrast (main effect) and exclude regions where there is a significant interaction between contrasts (P <0.05 uncorrected). Contrasts can be entered in a conjunction analysis only if they are orthogonal, i.e. independent. This type of analysis is used to identify common activation across contrasts, which are thought to reflect the presence of a common Cognitive Component of Interest (CCI) present in each contrast. Experiments 1, 2 and 3 utilised this type of conjunction analysis. The implementation of conjunctions was revised in SPM99. In this most recent version of the program the assumption of orthogonality of the contrasts entered in a conjunction is utilized to calculate a joint probability value. In fact, because conjunctions require orthogonal contrasts, the probabilities associated with each contrast are independent. Therefore, their joint probabilities are simply the product of their individual probabilities. For instance, if activation were present at a level of significance of P<0.1 uncorrected in three contrasts (A-B, C-D and E-F) one would likely consider the result as non­ significant, when considering each contrast individually because of the low significance. However, since the activation obtained in the three contrasts is an independent measure, the likelihood of all three activations being false positives is: P(A-B) * P(C-D) * P(E-F) = 0.1 * 0.1 * 0.1 = 0.001. While the SPM99 version of the conjunction analysis does not exclude the presence of an interaction between contrasts, it does assure, at a certain level of significance, activation is present in each of the considered contrasts.

The masking option (called inclusive masking in SPM99) ensures that voxels are only present in the statistical map if they are also significantly active in each of the contrasts specified as a mask.

The methods outlined in this Chapter are applicable to all of the experiments presented in this thesis. The experiment-specific linear contrasts formulated are described in the Method Sections for each Experiment.

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